The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N=2 black holes that contains the STU model.Comment: 14 page

CHL Dyons and Statistical Entropy Function from D1-D5 System

We give a proof of the recently proposed formula for the dyon spectrum in CHL string theories by mapping it to a configuration of D1 and D5-branes and Kaluza-Klein monopole. We also give a prescription for computing the degeneracy as a systematic expansion in inverse powers of charges. The computation can be formulated as a problem of extremizing a duality invariant statistical entropy function whose value at the extremum gives the logarithm of the degeneracy. During this analysis we also determine the locations of the zeroes and poles of the Siegel modular forms whose inverse give the dyon partition function in the CHL models.Comment: LaTeX file, 48 pages; v2: typos correcte

Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories

The spectrum of quarter BPS dyons in N=4 supersymmetric string theories can change as the asymptotic moduli cross walls of marginal stability on which the dyon can break apart into a pair of half BPS states. In this paper we classify these marginal stability walls and examine this phenomenon in the context of exact dyon spectrum found in a class of N=4 supersymmetric string theories. We argue that the dyon partition functions in different domains separated by marginal stability walls are the same, but the choice of integration contour needed for extracting the degeneracies from the partition function differ in these different regions. We also find that in the limit of large charges the change in the degeneracy is exponentially suppressed compared to the leading contribution. This is consistent with the fact that in the computation of black hole entropy we do not encounter any change as the asymptotic moduli fields move across the walls of marginal stability. Finally we carry out some tests of S-duality invariance in the theory.Comment: LateX file, 1 figure, 42 pages; v2 more tests of S-duality added with complete proof for all N<7; v3: minor change

Dying Dyons Don't Count

The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime supersymmetry are counted by a Siegel modular form. The pole structure of the modular form leads to a contour dependence in the counting formula obscuring its duality invariance. We exhibit the relation between this ambiguity and the (dis-)appearance of bound states of 1/2-BPS configurations. Using this insight we propose a precise moduli-dependent contour prescription for the counting formula. We then show that the degeneracies are duality-invariant and are correctly adjusted at the walls of marginal stability to account for the (dis-)appearance of the two-centered bound states. Especially, for large black holes none of these bound states exists at the attractor point and none of these ambiguous poles contributes to the counting formula. Using this fact we also propose a second, moduli-independent contour which counts the "immortal dyons" that are stable everywhere.Comment: 27 pages, 2 figures; one minus sign correcte

On the dyon partition function in N=2 theories

We study the entropy function of two N =2 string compactifications obtained as freely acting orbifolds of N=4 theories : the STU model and the FHSV model. The Gauss-Bonnet term for these compactifications is known precisely. We apply the entropy function formalism including the contribution of this four derivative term and evaluate the entropy of dyons to the first subleading order in charges for these models. We then propose a partition function involving the product of three Siegel modular forms of weight zero which reproduces the degeneracy of dyonic black holes in the STU model to the first subleading order in charges. The proposal is invariant under all the duality symmetries of the STU model. For the FHSV model we write down an approximate partition function involving a Siegel modular form of weight four which captures the entropy of dyons in the FHSV model in the limit when electric charges are much larger than magnetic charges.Comment: 48 page

Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds

We find the exact spectrum of a class of quarter BPS dyons in a generic N=4 supersymmetric Z_N orbifold of type IIA string theory on K3\times T^2 or T^6. We also find the asymptotic expansion of the statistical entropy to first non-leading order in inverse power of charges and show that it agrees with the entropy of a black hole carrying same set of charges after taking into account the effect of the four derivative Gauss-Bonnet term in the effective action of the theory.Comment: LaTeX file, 39 pages; minor change

Dyon Spectrum in N=4 Supersymmetric Type II String Theories

We compute the spectrum of quarter BPS dyons in freely acting Z_2 and Z_3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the effective action. The result is significant since in these theories the entropy of a small black hole, computed using the curvature squared corrections to the effective action, fails to reproduce the statistical entropy associated with elementary string states.Comment: LaTeX file, 32 pages; v2:minor change

Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime

We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s=1/2,1,2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.Comment: 31 page

Three String Junction and N=4 Dyon Spectrum

The exact spectrum of dyons in a class of N=4 supersymmetric string theories gives us information about dyon spectrum in N=4 supersymmetric gauge theories. This in turn can be translated into prediction about the BPS spectrum of three string junctions on a configuration of three parallel D3-branes. We show that this prediction agrees with the known spectrum of three string junction in different domains in the moduli space separated by walls of marginal stability.Comment: LaTeX file, 14 page

Black hole partition functions and duality

The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function'. We present this function in the presence of R^2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N=4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.Comment: 36 pages, Late